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Proof step 2 from proof band-011x-01 (previous step)

128 ≤ band(255, b2i(by)), 0 < band(255, b2i(by)), 0 ≤ band(255, b2i(by)), 0 < b2i(by) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ i → band(i, 255) = i % 256

Rule argument

seq: ⊦ 0 ≤ i → band(i, 255) = i % 256 subst: [i] → [b2i(by)] rotate: F spec: intops inst: name: band-255-pos

Additional information

Used simplifier rules: byte-mod-100x: ⊦ b2i(by) % 256 = b2i(by);%byte-nge: i ≥ 128 ⊦ ¬ (* i) ≤ b2i(by);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ band(i, j) = band(j, i); Used terms: b2i(by)